The rate of capital growth in a bank account is described by the differential equation(adsbygoogle = window.adsbygoogle || []).push({});

dM/dt = aM

Where dM/dt is the rate of change of the capital M and a is the annual interest rate.

Show that the general solution for the time dependence of capital M(t) is given by:

M(t) = M0 * e^at

where t is the time in years and M0 is the initial capital.

Really struggle with questions written like this, I know I should be approaching the question by integrating dM/dt = aM, but I dont understand where M0 comes into this atall, any help much appreciated!

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# Applications of Differential equations

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